Textured View Errors
This looks to me like it may an issue with being in multi-texture mode.
In multitexture mode, lighting is calculated per vertex. This means that the lighting on a giant plane is calculated at the corners. Because these are a long way from the light, this means the corners are black, and this extends towards the camera.

There are two ways I see to fix this if this is the case.
The first is to switch to GLSL mode. GLSL mode calculates lighting per screen-space pixel and provides much better looking results (also allows normal maps etc.)
The second is to try subdividing the plane such that the lighting resolution is higher. If your computer is old, this may be the only option to provide decent performance.



Another possible cause is mist. Again, in multitexture mode this is vertex based. Check that mist is disabled. You may have accidentally made your default blend file have a misty world.



A final possible problem may be your GPU or it's drivers. It may not be calculating mipmaps correctly in which case either a driver update may fix it, or using .dds textures (which contain pre-defined mipmaps) could solve it.



If none of these provide a solution, upload a blend file and I'll see if the issue is replicated on my computer